Summing next-to-next-to-leading logarithms in b->c transitions at zero recoil

Perturbative corrections to b->c transitions at zero recoil are considered in the two-step matching scheme. The matching coefficient for the b->c currents from the intermediate effective theory (between the scales m_b and m_c) to the low-energy effective theory (scales below m_c) has been found with two-loop accuracy. The next-to-next-to-leading logarithms has been summed in the leading order in m_c/m_b. Higher-order corrections are estimated in the large-beta_0 limit.